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An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.
Q. What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?
- a)12
- b)10
- c)13
- d)16
Correct answer is option 'A'. Can you explain this answer?
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An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 5...
It has been given that the customer has to receive 20 notes at the maximum. Also, we have restriction on the number of 500 rupee notes (fifty) but we do not have any restriction on the number of notes of other denominations. Therefore, in order to serve the maximum number of customers, we have to minimize the number of 500 rupee notes dispensed as much as possible.
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If no 500 rupee note is dispensed, then a minimum of 25 notes will be required (25 200 rupee notes).
If one 500 rupee note is dispensed, then a minimum of one 100 rupee note and twenty two 200 rupee notes will be required. The total number of notes required = 1 + 1 + 22 = 24. Therefore, we can eliminate this case.
If two 500 rupee notes are dispensed, then a minimum of 20 two hundred rupee notes will be required. We can eliminate this case as well since the number of notes required is greater than 20.
If three 500 rupee notes are dispensed, then a minimum of 1 hundred rupee note and 17 two hundred rupee notes will be required. The number of notes required in this case is 3+1+17 = 21. Therefore, we can eliminate this case as well.
If four 500 rupee notes are dispensed, then a minimum of 15 two hundred rupee notes will be required. Total number of notes required in this case is 4+15 = 19 < 20.="" therefore,="" this="" is="" a="" valid="" />
The least number of 500 rupee notes with which we can serve a customer such that the total number of notes dispensed does not exceed 20 is 4. Therefore, a maximum of [50/4] = 12 customers can be served with 50 five hundred rupee notes and hence, option A is the right answer.
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An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 5...
Understanding the ATM's Withdrawal Rules
To solve the problem, we need to analyze the rules of the ATM and the limitations imposed by the available stock of notes.
ATM Constraints
- The ATM dispenses Rs. 5000 per withdrawal.
- Each customer must choose a preferred denomination among 100, 200, or 500 rupee notes.
- The number of notes of the preferred denomination must exceed the total number of notes of the other denominations.
Available Notes
- The ATM has a stock of 50 notes of Rs. 500.
- We can use a sufficient number of Rs. 100 and Rs. 200 notes.
Maximum Notes per Withdrawal
- Each customer can withdraw using at most 20 notes in total.
Calculating the Maximum Customers
1. Using Rs. 500 Notes as Preference:
- If a customer prefers Rs. 500 notes, the maximum possible is just 10 notes (Rs. 500 x 10 = Rs. 5000).
- Other denominations would be 0, which does not satisfy the condition since Rs. 500 notes should exceed the total of others.
2. Using Rs. 200 Notes as Preference:
- If a customer prefers Rs. 200 notes, the maximum notes can be 25 (Rs. 200 x 25 = Rs. 5000).
- However, this exceeds the 20-note limit.
3. Using Rs. 100 Notes as Preference:
- If a customer prefers Rs. 100 notes, they can use 50 notes (Rs. 100 x 50 = Rs. 5000).
- But again, this exceeds the 20-note limit.
Optimal Strategy
- The most effective way is to maximize the use of Rs. 500 notes while ensuring the preferred denomination is greater than the others.
- By dispensing 10 customers with Rs. 500 notes, we use all 50 notes (1 per customer) and meet the condition.
Conclusion
- The maximum number of customers the ATM can serve is 10 when using Rs. 500 notes as the preferred denomination, which adheres to all rules and constraints of the problem. Thus, the correct answer is option A.
To solve the problem, we need to analyze the rules of the ATM and the limitations imposed by the available stock of notes.
ATM Constraints
- The ATM dispenses Rs. 5000 per withdrawal.
- Each customer must choose a preferred denomination among 100, 200, or 500 rupee notes.
- The number of notes of the preferred denomination must exceed the total number of notes of the other denominations.
Available Notes
- The ATM has a stock of 50 notes of Rs. 500.
- We can use a sufficient number of Rs. 100 and Rs. 200 notes.
Maximum Notes per Withdrawal
- Each customer can withdraw using at most 20 notes in total.
Calculating the Maximum Customers
1. Using Rs. 500 Notes as Preference:
- If a customer prefers Rs. 500 notes, the maximum possible is just 10 notes (Rs. 500 x 10 = Rs. 5000).
- Other denominations would be 0, which does not satisfy the condition since Rs. 500 notes should exceed the total of others.
2. Using Rs. 200 Notes as Preference:
- If a customer prefers Rs. 200 notes, the maximum notes can be 25 (Rs. 200 x 25 = Rs. 5000).
- However, this exceeds the 20-note limit.
3. Using Rs. 100 Notes as Preference:
- If a customer prefers Rs. 100 notes, they can use 50 notes (Rs. 100 x 50 = Rs. 5000).
- But again, this exceeds the 20-note limit.
Optimal Strategy
- The most effective way is to maximize the use of Rs. 500 notes while ensuring the preferred denomination is greater than the others.
- By dispensing 10 customers with Rs. 500 notes, we use all 50 notes (1 per customer) and meet the condition.
Conclusion
- The maximum number of customers the ATM can serve is 10 when using Rs. 500 notes as the preferred denomination, which adheres to all rules and constraints of the problem. Thus, the correct answer is option A.
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An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.Q. What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?a) 12b) 10c) 13d) 16Correct answer is option 'A'. Can you explain this answer?
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An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.Q. What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?a) 12b) 10c) 13d) 16Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.Q. What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?a) 12b) 10c) 13d) 16Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.Q. What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?a) 12b) 10c) 13d) 16Correct answer is option 'A'. Can you explain this answer?.
An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.Q. What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?a) 12b) 10c) 13d) 16Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.Q. What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?a) 12b) 10c) 13d) 16Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.Q. What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?a) 12b) 10c) 13d) 16Correct answer is option 'A'. Can you explain this answer?.
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An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.Q. What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?a) 12b) 10c) 13d) 16Correct answer is option 'A'. Can you explain this answer?, a detailed solution for An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.Q. What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?a) 12b) 10c) 13d) 16Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.Q. What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?a) 12b) 10c) 13d) 16Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.Q. What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?a) 12b) 10c) 13d) 16Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
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